Marvin Lewis attends a news conference after an NFL game...

Marvin Lewis attends a news conference after an NFL game in Cincinnati, in this Sunday, Dec. 16, 2018, file photo.  Credit: AP/Gary Landers

The Jets’ coaching search is starting to heat up.

They have interviewed a former longtime NFL head coach, are preparing to speak with one of the most highly regarded candidates and will talk with a surprise name who is very familiar to Jets fans.

Former Bengals coach Marvin Lewis interviewed with the Jets on Thursday. They will interview 49ers defensive coordinator Robert Saleh on Friday, according to the NFL Network. General manager Joe Douglas also has requested permission from the Saints to speak to defensive backs coach Aaron Glenn, who played eight seasons with the Jets.

Douglas promised to "cast a very wide net" in picking Adam Gase’s replacement, and he is doing just that.

Lewis wasn’t someone linked to the Jets, but he has ties to Douglas from Baltimore. The Jets are the first known team to show interest in Glenn for a head-coaching position this offseason. Saleh is a hot candidate who is drawing plenty of interest.

Saleh, 41, already has been interviewed by the Falcons and Lions. He’s also slated to speak with the Chargers and Jaguars for their vacancies.

A fiery coach whose passion is evident on the sideline, Saleh has been the 49ers’ defensive coordinator the past four seasons and has elevated his players into a top-five defense and passing defense the past two seasons.

Aaron Glenn #31 of the Jets runs with the ball...

Aaron Glenn #31 of the Jets runs with the ball during the game against Washington at Giants Stadium on Sept. 26, 1999. Credit: Getty Images/Ezra Shaw

Saleh’s defensive strategies and game plans helped the 49ers reach last year’s Super Bowl. They lost to Kansas City.

This season, the 49ers lost tackle DeForest Buckner in free agency and sack specialist Nick Bosa in Week 2 to a torn ACL (suffered at MetLife Stadium against the Jets). Cornerback Richard Sherman played in only five games. San Francisco finished fifth in total defense, fourth in passing defense and seventh in rushing defense.

Saleh was a defensive assistant on Pete Carroll’s staff in Seattle from 2011-13, and the Seahawks won the Super Bowl in Saleh’s last year there. He’s also worked with the Texans and Jaguars since joining the NFL in 2005.

Lewis became the second person the Jets have interviewed and the first known candidate who had previous NFL head-coaching experience. They interviewed Kansas City offensive coordinator Eric Bieniemy on Wednesday.

New Orleans Saints secondary coach Aaron Glenn calls to players...

New Orleans Saints secondary coach Aaron Glenn calls to players against the Philadelphia Eagles at Lincoln Financial Field on December 13, 2020 in Philadelphia, Pennsylvania. Credit: Getty Images/Tim Nwachukwu

Lewis, 62, coached Cincinnati from 2003-18. He went 131-122-3 and led the Bengals to the playoffs seven times. He also was the Ravens’ defensive coordinator from 1996-2001. (Douglas began his NFL career in Baltimore in 2000 as a scout.)

Lewis has spent the past two seasons working with former Jets coach Herman Edwards at Arizona State, first as a special adviser and this past year as co-defensive coordinator.

The Jets’ interest in Glenn is somewhat surprising, but he has done well in his current role with the Saints. Because New Orleans has a playoff game this weekend, the interview is expected to take place next week.

Glenn is completing his fifth season as the Saints’ defensive backs coach. The Saints ranked in the top five in passing defense and tied for the NFL lead in interceptions.

A first-round pick of the Jets in 1994, Glenn made two Pro Bowls as a cornerback while Bill Parcells was the coach. He also played for Houston, Dallas, Jacksonville and New Orleans and made another Pro Bowl.

Glenn retired after the 2008 season and returned to the NFL in 2012 with the Jets, serving as a scout for two years. He served as the Browns assistant secondary coach the next two years before joining the Saints in 2016.

The Jets also have requested permission to interview Bills offensive coordinator Brian Daboll, Colts defensive coordinator Matt Eberflus, Titans offensive coordinator Arthur Smith and Rams defensive coordinator Brandon Staley. All of their teams have playoff games this weekend.

More names are expected to be added to this list.

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